ARGUMENTS 

The term "argument" is ambiguous in that it has at least two meanings.  On the one hand, it is an activity that people engage in with others; on the other, it is a conclusion ostensibly supported by reasons or evidence.  It is only the latter meaning that is addressed herein.

1.   Argument: a specific combination of statements in which one or more statement is claimed to give evidence or reason for another

2.    Premises and Conclusions

a.            Premises -  those statements that are said to support the conclusion.

b.            Conclusion - the statement that is said to be supported by or to follow from the premises.

3.   Types of Arguments   

a.          Deductive – an argument in which a conclusion is said to follow necessarily from the premises, i.e., the premises entail the conclusion

b.          Inductive – an argument in which the the conclusion is said to be only probable, i.e., the premises support the conclusion without entailing it

4.   Standards

a.          Truth and Falsity: premises and conclusions are said to be either true or false[1]

b.          Validity: a deductive argument is valid in the case that if its premises are true its conclusion must be true.

c.          Soundness: a deductive argument is sound if it is valid and its premises are true.

d.          Strength: an inductive argument is strong if the truth of its premises make the truth of its conclusion highly probable.

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[1] Both classical and modern logic in their usual forms assume that any well-formed sentence is either true or false.  On a practical level this generally works quite well.  However, to see the shortcoming of this assumption do the following exercise:

Take out a piece of paper and on one side – label it “A” - write
    “The statement on B is true.”
On the other side – label it “B” - write
    “The statement on A is false”

If we assume the statement on A to be true, viz., that the statement on B is true, then according to the statement on B, A is false.  If we assume, on the other hand, that the statement on A is false, viz., that it is false that the statement on B is true, then it is not true “The statement on A is false” as asserted by the statement on B.  In other words, starting from the seemingly correct assumption that statements are either true or false we end in contradiction.  If we assume A to be true then A is false.  If we assume A to be false, then A is not false.  This is what has been called a “Strange Loop” – a loop of reasoning that cannot be resolved because to accept the statements as either true or false loops around to its opposite.  From this perspective, the statements are neither true nor false – they are inherently undecidable or indeterminate.  N. Kathrine Hayles, The Cosmic Web: Scientific Field Models & Literary Strategies in the 20^th Century (Cornell University Press, 1984), p. 34.